多主从群体博弈中合作均衡的存在性

基于Scarf,Kajii关于n-人非合作博弈中的合作均衡存在性定理,越来越多的研究表明,对非合作博弈的合作均衡研究是有必要的.本文综合Sandholm的群体博弈模型以及Yang和Ju证明的多主从博弈的合作均衡存在性定理,旨在详细研究多主从群体博弈的合作均衡.首先,在多主从群体博弈中引入合作均衡的概念,并通过Kajii...     

多目标大博弈中弱Pareto-Berge均衡的存在性

研究了具有任意多个局中人的非合作多目标博弈(多目标大博弈).基于一般非合作博弈中的Berge均衡概念,定义多目标大博弈中的弱Pareto-Berge均衡.进一步推广了截口定理,得到新的截口定理,并且利用这个新的截口定理证明多目标大博弈中弱Pareto-Berge均衡的存在性.多目标大博弈中弱Pareto-Nash均衡的存在性结论可作为弱Pareto-Berge均衡存在性的特例给出.     

伪连续条件下不确定性非合作博弈Nash-Slater均衡的存在性

从两个角度研究了伪连续条件下不确定性n人非合作博弈的Nash-Slater(NS)均衡的存在性.在不确定博弈中,分别利用伪连续函数的最大值定理以及伪连续下的Ky Fan不等式,得到了两个伪连续支付下的NS均衡存在性定理.     

不确定下广义博弈强Berge均衡的存在性

本文基于不确定下的非合作博弈NS均衡给出了不确定下广义非合作博弈强Berge均衡与广义多目标弱Pareto强Berge均衡的定义,利用Fan-Glicksberg不动点定理证明了不确定下广义非合作博弈强Berge均衡与不确定下广义多目标弱Pareto强Berge均衡存在性定理.     

不确定性下强Berge均衡的存在性

在已知不确定参数变化的范围下,研究了非合作博弈与广义非合作博弈的强Berge均衡的存在性,基于强Berge均衡与不确定性下非合作博弈的强Nash均衡的概念,给出了不确定参数下非合作博弈与广义非合作博弈的强Berge均衡的定义,并利用Fan-Glicksberg不动点定理证明其存在性,最后用算例验证其可行性.     

大博弈中Nash均衡的存在性

研究了具有任意多个局中人的非合作博弈(大博弈)中Nash均衡的存在性.将1969年Ma的截口定理推广得到新的截口定理.用这个新的截口定理进一步证明了:1)大博弈中Nash均衡的存在性;2)纯策略集为紧度量空间而且支付函数为连续函数时,连续大博弈中混合策略Nash均衡的存在性.并且存在性定理推出了2010年Salonen的结果,即此研究结果较Salonen的结论更具普遍意义.     

超级模数博弈的存在性

本文定义了一类在有序Banach空间上的超模博弈,并利用著名的Birkhoff不动点定理证明了有序Banach空间上超模博弈Nash均衡的存在性.     

轻微利他弱Pareto-Nash均衡

2008年,Marco和Morgan在正规型博弈中引入轻微利他均衡和友好均衡的概念.利用轻微利他的思想,研究多目标博弈.证明轻微利他弱Pareto-Nash均衡的存在性定理,进一步地讨论轻微利他弱Pareto-Nash均衡和本质均衡的关系.     

年龄分布下种群资源开发动态博弈的Nash均衡

研究具有年龄结构的种群资源开发中的动态博弈问题.应用~Kakutani~多值映射不动点定理证明了Nash均衡的存在性,借助切锥－法锥和共轭系统技巧刻画了均衡策略.结果表明,在一定条件下,均衡策略具有Bang-Bang结构.     

两阶段主从博弈均衡解的存在性

首先给出带参数的纳什均衡问题Γ(x),在此基础上给出了具有带参数的纳什均衡约束的两阶段主从博弈问题G.可以证明带参数的纳什均衡点是存在的,即无论领导者选择何种策略,跟随者的最佳回应集都是非空的.最后推出了关于两阶段主从博弈均衡点的存在性定理.     

一种n人静态博弈纯策略纳什均衡存在性判别法

本首先给出了n人静态博弈纯策略纳什均衡存在的充要条件。然后给出n人静态博弈纯策略纳什均衡存在性的一种判别方法。最后在判别纯策略纳什均衡存在的条件下，给出判定该静态博弈存在多少纯策略纳什均衡以及哪些纯策略组合是纯策略纳什均衡(解)的方法。     

Split equilibrium problems for related games and applications to economic theory

ABSTRACT

In this paper we introduce the concept of split Nash equilibrium problems associated with two related noncooperative strategic games. Then we apply the Fan-KKM theorem to prove the existence of solutions to split Nash equilibrium problems of related noncooperative strategic games, in which the strategy sets of the players are nonempty closed and convex subsets in Banach spaces. As an application of this existence to economics, an example is provided that studies the existence of split Nash equilibrium of utilities of two related economies. As applications, we study the existence of split Nash equilibrium in the dual (playing twice) extended Bertrand duopoly model of price competition.     

集值映射的Nash平衡点的存在定理

本文引入了集值映射的Nash平衡点的概念，它以通常的Nash平衡点及Loose Nash平衡点为特例，并在紧和非紧的假设下，得到集值映射的Nash平衡点的存在定理，其中在非紧的情况下使用escaping序列的定义．     

一个带产品定价约束的竞争选址双层规划模型及其求解算法

以大型连锁卖场的选址为研究背景,提出了一个在竞争环境下使获利最大的竞争选址定价双层规划模型,其中上层模型做出选址决策,下层模型确定产品的纳什均衡价格.将设施效用引入到模型中,用指数效用函数来刻画顾客的购物行为偏好,首次证明了不合作状态下双方价格均衡解的存在性和唯一性,并给出了求解最优设施点设置方案和价格均衡解的算法思想及数值算例.     

A minimally altruistic refinement of Nash equilibrium

We introduce a minimal notion of altruism and use it to refine Nash equilibria in normal form games. We provide three independent existence proofs, relate minimally altruistic Nash equilibrium to other equilibrium concepts, conduct an in-depth sensitivity analysis, and provide examples where minimally altruistic Nash equilibrium leads to improved predictions.     

On Nash Equilibrium Strategy of Two-person Zero-sum Games with Trapezoidal Fuzzy Payoffs

In this paper, we investigate Nash equilibrium strategy of two-person zero-sum games with fuzzy payoffs. Based on fuzzy max order, Maeda and Cunlin constructed several models in symmetric triangular and asymmetric triangular fuzzy environment, respectively. We extended their models in trapezoidal fuzzy environment and proposed the existence of equilibrium strategies for these models. We also established the relation between Pareto Nash equilibrium strategy and parametric bi-matrix game. In addition, numerical examples are presented to find Pareto Nash equilibrium strategy and weak Pareto Nash equilibrium strategy from bi-matrix game.     

双人静态博弈纯战略纳什均衡存在性判别

本文给出了双人有限静态博弈纯战略纳什均衡存在性的一种判别方法。并且，在纳什均衡存在的条件下，本判别法将给出纳什均衡解及解的唯一性判别。     

Noncooperative Games with Vector Payoffs Under Relative Pseudomonotonicity

We consider the Nash equilibrium problem with vector payoffs in a topological vector space. By employing the recent concept of relative (pseudo) monotonicity, we establish several existence results for vector Nash equilibria and vector equilibria. The results strengthen in a major way existence results for vector equilibrium problems which were based on the usual (generalized) monotonicity concepts.     

Generalising diagonal strict concavity property for uniqueness of Nash equilibrium

In this paper, we extend the notion of diagonally strictly concave functions and use it to provide a sufficient condition for uniqueness of Nash equilibrium in some concave games. We then provide an alternative proof of the existence and uniqueness of Nash equilibrium for a network resource allocation game arising from the so-called Kelly mechanism by verifying the new sufficient condition. We then establish that the equilibrium resulting from the differential pricing in the Kelly mechanism is related to a normalised Nash equilibrium of a game with coupled strategy space.